LAB OBJECTIVES:

1. Introduce decision modeling for conservation

2. Define the basic decision problem

3. Consider the impacts of uncertainty on DM

4. Introduce learning and adaptive management

Introduction

In these exercises apply concepts of quantitative decision modeling to problems in conservation biology. These, and later problems in harvest decision making, share at least 2 features: (1) there are (or should be) an explicit objective, and (2) there is uncertainty as to what the results will be of any given decision (conservation action). Conservation problems often seem to be more complex than "simple" harvest problems, particularly in the definition of objectives and the modeling of biological processes, but as we shall see these often can be expressed in relatively simple form.

To run the exercises, you will need a flexible, graphically-oriented program called Netica, available from Norsys. This program has already been installed on the lab computers. However, If you are running these exercises from outside the lab you will need to go to the Norsys download page and download and install the ‘limited’ version of Netica (free of charge); a fully-enable version of Netica may be ordered at this site, but the limited version will work fine for all of our class examples.

Note 1: Netica needs to have been installed on your system to run these exercises. It is helpful if you have opened the Netica program at least once previously; that way your computer seems to "remember" that the *.dne files in the web page associate with Netica. However, occasionally when you click on an example link you will get plain text code instead of a nice graphic display. If that happens click the back arrow on your browser, then go back forward to the page and again. Usually this works.

Note 2: Netscape browsers do not seem to work reliabily with this program. We suggest that if you are using Netscape you quit and install a recent version of Internet Explorer.

States, Decisions, Objective

To review, we will start with a simple, non-dynamic decision, and definition of some terms. In general, we are going to examine the state of some natural resource system, and make a decision in order to meet some objective. By state we simply mean some description of the nature or status of the system we are interested in. Examples of states include: total abundance, abundance by age class, acres of habitat, total biomass of a forest, basal area, and so on. An objective is some outcome that we desire to achieve. Examples include maximum sustainable harvest, maximum net annual income, minimum probability of extinction, and so on. A decision is some action we are taking that presumable will lead us toward reaching our objective.

Let's begin with a very simple conservation decision (con1.dne) We are faced with the potential loss of an endangered species, and two alternatives are available: the design and management of a 100 km² reserve ("reserve"), and a "do nothing" alternative ("nothing"), and that the species is extant at the time of the decision, but imperiled. Given either of the alternative decisions, there are two possible outcomes: the population persists and possibly increases in abundance ("persists"), or the population declines to local extinction ("extinct').

Each combination of a decision and outcome has associated with it potential costs (e.g., reserve construction) and benefits (e.g., species persistence), which are incorporated into a utility function U that depends on both the decision and its outcome. From the point of view of endangered species management, population persistence is always preferable to extinction, and the best situation might involve persistence along with no action. On the other hand, the worst situation might involve no action and extinction, because of the ramifications (e.g., lawsuits, negative publicity) of inaction followed by extinction. The specific values for each decision-outcome combination require will vary depending on the decision maker's perspective. We have assigned the values for this problem as

	Utility
	Persist	Extinct
Reserve	70	20
Nothing	100	0

where the entries may be dollars, or simply the relative value of the outcome on a 0-100 scale (0= worst 100=best).

In the event that decision-specific outcomes are certain (i.e., the consequences of conservation and inaction are known), a determination of the optimal decision becomes a straightforward comparison of the corresponding utilities. For now, we are assuming that the management is certain to result in population persistence, whereas inaction is certain to lead to extinction.

	Probability
	Persist	Extinct
Reserve	1	0
Nothing	0	1

Since the respective utilities are 70 and 0 respectively (in bold in the table), the optimal decision is to build and maintain the reserve; this is confirmed by examining the values next to each decision in the network.

Of course, the outcome of decision making with biological systems is almost never certain. Assume here that environmental factors influence population dynamics through their effects of reproduction and mortality. The essentially random nature of environmental variation induces uncertainty in population dynamics, and thus in the likelihood of persistence. At least conceptually, these uncertainties can be represented by assigning probabilities to the possible outcomes, based on an assumed model of population dynamics and available field data. Often there will be a great deal of uncertainty about the impact of the decision. Let's take an extreme (but not completely unrealistic) case, in which we assume that the chances of persistence are no better than the flip of a coin, regardless of the decision. That is:

	Probability
	Persist	Extinct
Reserve	0.50	0.50
Nothing	0.50	0.50

At first glance, it appears that our decision could also be made by coin flip. However, that would be true only if we valued each outcome equally, and we don't. The network con2.dne describes this problem ( be sure to compile the network with the 'lighting strike" and select "unknown" for the reserve decision and other boxes). The expected values for each decision are displayed in the right column. These are computed by:

E(U| Reserve) = U(Reserve, Persist) Prob (Persist|Reserve)+U(Reserve, Extinct) Prob (Extinct|Reserve) = 70(0.5)+ 20(0.5)= 45

and

E(U| Nothing) = U(Reserve, Nothing) Prob (Persist|Nothing)+U(Reserve, Nothing) Prob (Extinct|Nothing) = 100(0.5)+ 0(0.5)= 50

Again, Netica performs these calculations; clearly the optimal decision under these assumptions is to do nothing.

Two things should be obvious at this point:

Even when practically nothing is known about the system (the coin flip analogy) we still have a way of deciding what to do (select the decision that maximizes expected utility)
Changing either the utilities or the outcome probabilities may change the optimal outcome.

Student exercise 1: Change the values in the utility function as below; what is the new optimal decision, and what is its value?

(To edit the utility table, 1) double click on the utility node, 2) click on "table" in the pop-up window, 3) change the values then click "apply", 4) recompile with the lighting strike; if you wish to save this give it another name and save on your local or network directory).

	Utility
	Persist	Extinct
Reserve	100	5
Nothing	100	0

Just as optimal decision making is influenced by the utility function, so also is it dependent on patterns in the outcome probabilities. With the earlier utilities (as in con1.dne and con2.dne) and with the same outcome probabilities for each decision, we had E(U|nothing)= 0.5 and E(U|reserve) =0.45, so that an optimal decision is not to develop a conservation reserve. If, however, the conservation option is assumed to increase the persistence probability, then conservation actions which otherwise would be too costly to undertake might be justified. Specifically, the probabilities:

	Probability
	Persist	Extinct
Reserve	0.65	0.35
Nothing	0.50	0.50

are encoded in con3.dne; these incorporate the assumptions of 1) enhancement of persistence with the reserve in place, and 2) no change in the chance of extinction under the "nothing" alternative.

Student exercise 2: What is the new optimal decision, and its expected value, for the above probabilities?

Decision-making with Model Uncertainty

Thus far we have assumed that there is a single, distinctive relationship between a decision and its outcome, recognizing uncertainties attendant to random environmental variation. Our decision analyses have assumed that either persistence and extinction are uninfluenced by decisions (con2.dne), or else conservation leads to an increased probability of persistence (con3.dne). Both hypotheses allow for the potential effect of environmental variation, but neither takes into account the uncertainties about which hypothesis more appropriately represents the relationship between a decision and its outcomes. This is a key limitation, because uncertainty about the linkages between decision-making and its consequences lies at the heart of many controversies in natural resource conservation.

One way to handle process uncertainty is simply to incorporate alternative hypotheses directly into the decision analysis, with hypothesis weights or "likelihoods" representing a decision maker's confidence in the hypotheses. Consider, for example, the two hypothesized responses mentioned above: (1) persistence and extinction are equiprobable and unaffected by the decision (Model 1); and (2) persistence is more likely with conservation than without it (Model 2). Recall that the optimal decision under Model 1 is to take no action, whereas the optimal decision under hypothesis Mode 2 is to establish and maintain a reserve. An optimal decision that accounts for both hypotheses can be identified by comparing average utility values for each decision, except that now the averaging includes weights representing the uncertainty about which model is "true." The network in con4.dne encapsulates these ideas, under a scenario in which the probabilities of extinction/ persistence differ depending on which model is true.

	Probability (Assuming Model 1)		Probability (Assuming Model 2)
	Persist	Extinct	Persist	Extinct
Reserve	0.50	0.50	0.65	0.35
Nothing	0.50	0.50	0.50	0.50

Initially let's assume that we are completely ignorant about what model is "true" so that Prob(Model1) = Prob(Model2) = 0.50. We then get the expected values for each decision as displayed in con4.dne , in which the expectations now have to take into account both the uncertain outcomes (under each model) as well as uncertainty about which model is true. For example:

E(U|reserve) = E(U|reserve assuming Model 1) P(Model 1) + E(U|reserve assuming Model 2) P(Model 2) = 45(0.5) + 52.5(0.5)= 48.75.

The expected value of the "nothing" decision remains the same, since the outcome probabilities are not model-dependent for that action. In this example, then, giving both models equal weight results in the "nothing" decision as being optimal. Note however that the expected values are a bit closer (48.75 vs. 0.5) then under full belief in Model 1 (45 vs. 50). At some point as the evidence begins to favor Model 2, the decision should change.

Student exercise 3: Change the model weights from 50-50 to 25-75 in favor of Model 2. What is the new optimal decision, and its expected value, given these revised model probabilities?

Adaptive Updating

As suggested above, a knowledge of the model weights is important; any information that changes these weights potentially will influence decision making. One way that we can obtain this updated information is to make a decision (usually this will be the one that is apparently optimal) and then observe what happens following the decision.

In our simple example, each model makes a prediction about how likely persistence will be following each management action. Suppose that we make the decision to build the reserve (in this example, we're going to do that even though it is not the optimal decision). We then observe at the next monitoring period that the population has gone extinct. To see the impact on model weights, go to the network con4.dne and click on the "reserve" decision and "extinct" for the population status. The new model weights should now be 58.8 and 41.2 (Prob[Model 1]=0.588 and Prob[Model 2] =0.412).

Student exercise 4: Suppose that the "reserve" decision is made and the population persists (as measured at the next monitoring occasion). What are the new model weights ( Prob[ Model 1] and Prob [Model 2])? Compare this to the result you get when the "nothing" decision is made. This time do the model weights change? Why do you think that they do (or do not)?

You are probably asking yourself now: what good is a monitoring and updating program that has to wait to see if the population goes extinct before information feedback can occur? Also, if I decide to build (or not build a reserve) I've made a long term commitment- I can't change my mind just because model weights change. These are very good questions, and the answer really has 2 parts.

First, in practice we usually are evaluating persistence periodically, at a local spatial scale, in which case the absence of the animal in any particular geographic space at any survey time may not indicate global extinction (even assuming that our survey is a perfect census).

Second, in many instances the conservation decision is not an all-or-nothing proposition. We are frequently faced with series of decisions over time, each of which potentially can benefit from "learning" based on previous management actions. In the case of the harvest problem, the benefit of this was clear-cut: we always have the opportunity each year to adjust harvest rates in response to changing model beliefs, providing greater future harvest benefit. In a conservation problem involving long term commitments, we often cannot revise our management on a particular site, but we may be able to apply learning from that site to a future decision at another site.

Consider a reserve problem like the previous one, except that now we are faced with 2 sequential decisions involving 2 different potential reserves, both of which may influence the chances of the species' persistence (spatial_update.dne). Decision 1 is whether to build the first reserve, and Decision 2 (made at a later time) is whether to build the second. Let's suppose that at the first decision, we have (perhaps based on previous empirical work) greater (70%) belief in Model 2 than in Model 1. In this case, the expected value of "Reserve" for Decision 1 is slightly higher than "Nothing" (100.5 vs. 100.25), so we build the reserve. Suppose we then observe that the species persists (Status 1= persists). Notice that the model weights have changed: they are now 24.8 - 75.2 in favor of Model 2. Notice too that the expected value of Decision 2 now changes: evidence as a result of the previous decision has "fed back" into decision making. We again make the apparently optimal decision (Reserve) and observe what happens (persistence or extinction). For example, if the species persists at the second reserve, the model weights now change to 20.2 - 79.8.

Student exercise 5: Describe the impact of the following sequence of decisions and observations on the relative belief in Model 1 and Model 2 (following all decisions and observations):

Decision 1	Status 1	Decision 2	Status 2	P(Model1)	P(Model1)
Reserve	Persist	Nothing	Persist
Reserve	Persist	Reserve	Extinct
Reserve	Extinct	Reserve	Extinct
Nothing	Persist	Reserve	Extinct
Reserve	Persist	Nothing	Extinct
Reserve	Persist	Reserve	Persist

Additional reading

Conroy, M.J., and B.R. Noon. 1996. Mapping of species richness for conservation of biological diversity: conceptual and methodological issues. Ecological Applications 6:763-773.